Question

t

n

= a + (n - 1)d

∴ t

3

= a + (3 - 1)d = a + 2d

t

7

= a + (7 - 1)d = a + 6d

∴ t

3

+ t

7

= (a + 2d) + (a + 6d) = 2a + 8d

∴ 2a + 8d = 6

∴ a + 4d = 3 ..........(I)

t

3 × t

7

= (a + 2d) (a + 6d)

= (a + 4d - 2d) (a + 4d + 2d)

= (3 - 2d) (3 + 2d) .......... from (I)

∴ (3 - 2d) (3 + 2d) = 8

∴ 9 - 4d 2

= 8

∴ 4d2

= 1 d2

=

1

4 d =

1

2 or d = -

1

2

Now, if d =

1

2

a + 4 ×

1

2 = 3 .......... from (I)

a = 1

If d = -

1

2

a + 4 ×











1

2 = 3 .......... from (I)

a = 5

∴ the first term of the A. P. is 1 and the common difference is 1

2 .

or, the first term of the A. P. is 5 and the common difference is - 1

2​

Answer 1

ye question hai ya answer

post the question clearly

Answer 2

ye Kya hai question ya for answer